I recently saw a version of this puzzle in IEEE Potentials magazine. It caught my interest not only because it is a cute situation, but also because their published solution is wrong (or at least incomplete)!

Suppose you have a square box like the one illustrated below. The insides of the walls of the box are mirrored. Positioned in the center of the left wall is a laser pointer aimed at some angle θ. The laser beam bounces around inside the box and may eventually hit the spot from which it started.

For which values of θ will the laser beam eventually return to its starting point? Find all such values of θ. Solution.